A generalization to Sylow permutability of pronormal subgroups of finite groups

[EN] In this note, we present a new subgroup embedding property that can be considered as an analogue of pronormality in the scope of permutability and Sylow permutability in finite groups. We prove that finite PST-groups, or groups in which Sylow permutability is a transitive relation, can be characterized in terms of this property, in a similar way as T-groups, or groups in which normality is transitive, can be characterized in terms of pronormality.

Electronic version of an article published as Journal of Algebra and Its Applications, 2020, 19:03 https://doi.org/10.1142/S0219498820500528 © World Scientific Publishing Company.